Iron alloys of volatile elements in the deep Earth’s interior

Investigations into the compositional model of the Earth, particularly the atypical concentrations of volatile elements within the silicate portion of the early Earth, have attracted significant interest due to their pivotal role in elucidating the planet’s evolution and dynamics. To understand the behavior of such volatile elements, an established ‘volatility trend’ has been used to explain the observed depletion of certain volatile elements. However, elements such as Se and Br remain notably over-depleted in the silicate Earth. Here we show the results from first-principles simulations that explore the potential for these elements to integrate into hcp-Fe through the formation of substitutional alloys, long presumed to be predominant constituents of the Earth’s core. Based on our findings, the thermodynamic stability of these alloys suggests that these volatile elements might indeed be partially sequestered within the Earth’s core. We suggest potential reservoirs for volatile elements within the deep Earth, augmenting our understanding of the deep Earth’s composition.

This Supplementary Information contains eleven Supplementary Figures, five Supplementary Tables and Supplementary References, summarized as follows.
-Supplementary Fig. 1 -Elemental abundance in the silicate Earth versus formation enthalpy of the Fe alloys with a substitution ratio of 1/128 (Fe127X) at 20, 150 and 300 GPa.
-Supplementary Fig. 3 -Elemental abundance in the silicate Earth versus stabilities of the Fe alloys with a substitution ratio of 1/128 (Fe127X) at 20, 150 and 300 GPa.
-Supplementary Fig. 4 -Comparison of primary wave velocities with different doping elements at 300 GPa.
-Supplementary Fig. 5 -Comparison of bulk sound velocities with different doping elements at 300 GPa.
-Supplementary Fig. 6 -Comparison of the Possion's ratios with different doping elements at 300 GPa.
-Supplementary Fig. 7 -Comparison of the shear moduli with different doping elements at 300 GPa.
-Supplementary Fig. 8 -Crystal structures of the simulation models.
-Supplementary Fig. 11 -Mean square displacement (MSD) of Fe-As and Fe-Se systems.
-Supplementary Table            Table S1.Classification of the elements.The elements that we have considered in both main teet and supplementary information are all included.Volatility of elements is classified according to 50% condensation temperatures (Tc) at 10 -4 bar.In the current manuscript, we more focused on lithophile and chalcophile elements (non-siderophile elements as noted in the teet) with moderate and high volatility, which are marked in green.

Figure S1 .
Figure S1.Elemental abundance in the silicate Earth versus formation enthalpy of the Fe alloys with a substitution ratio of 1/128 (Fe127X) at 20, 150 and 300 GPa.Elemental abundances in the silicate Earth are ratioed to those in CI carbonaceous chondrites and normalized to [] ℎ []  = 1.0.

Figure S2 .
Figure S2.Elemental abundance in the silicate Earth versus formation enthalpy of the Fe alloys with a substitution ratio of 1/54 (Fe53X) and 1/128 (Fe127X) at 20, 150 and 300 GPa.(a), (b) and (c) represent substitution ratio of 1/54 at 20, 150 and 300 GPa, respectively.For easier comparison, the points from model Fe127X (in Figure S1) are plotted together with the points from model Fe53X on (d), (e) and (f) at 20, 150 and 300 GPa, respectively.

Figure S3 .
Figure S3.Elemental abundance in the silicate Earth versus stabilities of the Fe alloys with a substitution ratio of 1/128 (Fe127X) at 20, 150 and 300 GPa.(a), (b) and (c) represent the results calculated at 20, 150 and 300 GPa, respectively.Elemental abundances in the silicate Earth are ratioed to those in CI carbonaceous chondrites and normalized to [] ℎ []  = 1.0 .The horizontal aees are the terms of ∆ − ∆  with different temperatures of 2000, 4000 and 6000 K at 20, 150 and 300 GPa, respectively.The red dashed lines represent the fitting of the data.Here, we focus on the slope of this fitting line: a positive slope indicates a positive correlation between the depletion of elements and the stability of the alloy, while a negative slope suggests the opposite.The slope of the fitting line is 6.5*10-4, 0.017 and 0.028 for 20, 150 and 300 GPa, respectively.Elements locate in shaded areas indicate that their alloys satisfy ∆ − ∆  < 0 under the corresponding conditions.

Figure S4 .
Figure S4.Comparison of primary wave velocities with different doping elementsat 300 GPa.The substitutional ratio of these Fe alloys is 1/128 with a structure of FigureS1(a).For light elements, such as P and Si, would have an increasing effect on VP of pure Fe.For other heavy elements, the VP would be decreased after doping due to the increased density.

Figure S5 .
Figure S5.Comparison of bulk sound velocities with different doping elements at 300 GPa.The substitutional ratio of these Fe alloys is 1/128 with a structure of Figure S1(a).

Figure S6 .
Figure S6.Comparison of the Possion's ratios with different doping elements at

Figure S8 .
Figure S8.Crystal structures of the simulation models.The structures of the simulation models Fe128-nXn (n=1, 2, 3, 4, 5 and 6, for a, b, c, d, e and f, respectively).Red and brown spheres represent impurity and Fe atoms, respectively.These structures are generated by special quasi-random structure (SQS) technique1,2 .In these alloys, impurities atoms substitute Fe atoms randomly.(g) and (h) represent the models of Fe140X4 and Fe144X4, respectively.For each kind of impurity atom, the structure geometry optimizations based on the framework of density functional theory (DFT) would be generated independently.

Figure S9 .
Figure S9.Comparision of the calculated shear wave velocity (Vs) for hcp-Fe, FeC0.0625,FeO0.0625,Fe0.9375Si0.0625at 0 K and high temperatures.Black solid line represents pure Fe, dash lines represent Fe alloys in previous works and red open squares represent the alloys in Figure 4b.

Figure S11 .
Figure S11.Mean square displacement (MSD) of Fe-As and Fe-Se systems.We have also performed addition simulations to randomly distribute the doping elements within the simulated cell, where we create a 2×2×1 supercell of 36 atoms (the simulated cell contains 144 atoms) and each a supercell of 36 atoms contains a doping element.Mean square displacement (MSD) of X and Fe in Fe144X4 and Fe140X4 at ~330 GPa and 6000 K could represent interstitial and substitutional models respectively.MSDs of (a), As and Fe in Fe144As4; (b), As and Fe in Fe140As4; (c), Se and Fe in Fe144Se4 and (d), Se and Fe in Fe140Se4.The MSDs of As and Se and Fe increase obviously with simulation time indicating a liquid state for the interstitial model, while the MSDs of the substitutional model show a solid state under Earth's inner core condition.

Table 5 -
-Classification of the elements.List of the elements and their atomic radii.

Table S2 .
Spin test calculations.The calculated enthalpies of Fe53Si with and without spin at 20, 150 and 300 GPa.

Table S3 .
Formation enthalpies of the alloys.The calculated formation enthalpy (eV/atom) of the alloys with a substitution ratio of 1/128 (Fe127X) at 20, 150 and 300 GPa.

Table S4 .
Elastic properties of the alloys.Densities (ρ), elastic constants (Cij), moduli (B and G) and Poisson's ratio of the representative models at 300 GPa and 0K.